Nonconvex quasi variational inequalities. (English) Zbl 1206.49011

Summary: We introduce and consider a new class of quasi variational inequalities, which is called the nonconvex quasi-variational inequality. We show that the projection method can be used to establish the equivalence between the nonconvex quasi-variational inequalities, fixed points problems and the Wiener-Hopf equations. We use this equivalent alternative formulation to suggest and analyze a new class of two-step iterative methods for solving the nonconvex variational inequalities. We discuss the convergence of the iterative method under suitable conditions conditions. Our method of proof is very simple as compared with other techniques.


49J40 Variational inequalities
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
47H10 Fixed-point theorems